What is the Sum of Squares within group?What is the Mean Square between group? What is the Mean Square within group? Go through the steps of ANOVA hypothesis testing to see if you can conclude that there is adifference among population means. Let a = 0.05.Research by Singh et al. as reported in the journal Clinical Immunology and Immunopathologyis concerned with immune abnormalities in autistic children. As part of their research they tookmeasurements on the serum concentration of an antigen in three samples of children, all ofwhom were 10 years old or younger. The results in units per milliliter of serum follow.Autistic Children: 755, 385, 380, 215, 400, 343, 415, 360, 345, 450, 410, 435, 460, 360, 225Normal Children: 165, 390, 290, 435, 235, 320, 330, 205, 375, 345, 305, 220, 270, 355, 360Mentally RetardedChildren: 380, 510, 315, 565, 715, 380, 390, 245, 155, 335, 295, 200, 105, 105, 245

Excel Procedure: Enter the data for Autistic, Normal and Mentally in Excel sheet>Go to Data…

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Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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What is the Sum of Squares within group?

What is the Mean Square between group?

What is the Mean Square within group?

Go through the steps of ANOVA hypothesis testing to see if you can conclude that there is a
difference among population means. Let a = 0.05.
Research by Singh et al. as reported in the journal Clinical Immunology and Immunopathology
is concerned with immune abnormalities in autistic children. As part of their research they took
measurements on the serum concentration of an antigen in three samples of children, all of
whom were 10 years old or younger. The results in units per milliliter of serum follow.
Autistic Children: 755, 385, 380, 215, 400, 343, 415, 360, 345, 450, 410, 435, 460, 360, 225
Normal Children: 165, 390, 290, 435, 235, 320, 330, 205, 375, 345, 305, 220, 270, 355, 360
Mentally Retarded
Children: 380, 510, 315, 565, 715, 380, 390, 245, 155, 335, 295, 200, 105, 105, 245

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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